This invention relates to CORDIC rotations, and more particularly to CORDIC implementations for rotations over the complex field.
CORDIC algorithms are known for rotating complex numbers over the real field. It is intended that the term rotation as used throughout this specification encompass more general transformations. The acronym CORDIC comes from coordinate rotation digital computation. CORDIC algorithms perform rotations using only bit operations such as shifts and adds. Multiplications are eliminated. In CORDIC algorithms, a rotation is broken up ito a seqeunce of minirotations whose sum equals the desired rotation. As is well known, each of the mini rotations can be computed utilizing only bit operations. For a discussion of CORDIC algorithms, see, "Fourier Transform Computers Using CORDIC Iterations" IEEE Transactions on Computers, Vol. C-23, No. 10, October 1974.
It is well known that simple CORDIC hardware architecture can be used to implement (i,j)--plane (2-dimensional) rotations over the real field. Heretofore, however, there was no known CORDIC architectures for implementing (i,j)--plane rotations over the complex field.
It is therefore an object of the present invention to provide a CORDIC implementation for a known transformation matrix for complex field rotations.
Yet another object of the invention is to provide a CORDIC implementation for a different transformation matrix for (i,j)--plane rotations over the complex field.
Still another object of the invention is an optimum CORDIC implementation which requires only four times the hardware that is needed for rotation over the real field.